I understand that vacuums can be responsible for the temporary creation of particles. What I do not understand is how those particles could expand and become our current universe.
If you understand the first part, 'temporary particles', please explain to me! [LOL]
For the record, nobody really knows that! We believe Heisenberg uncertainty and quantum jitters at Planck scales [quantum foam] sets some limits at small scales, but why is that?? And why do those models break down at the Big Bang and at the singularities of black holes?? Something is wrong but a solution, a more fundamental explanation, awaits a theory of quantum gravity.
Consider this a corollary to MarkM's post above:
An observer can detect new particles three ways: by simply accelerating herself, by observing an accelerating/expanding spacetime, by observing an accelerating causal horizon. Are those real of just mathematical constructs?/ I am not sure.
But I do know different spacetimes [Rindler, Schwarszschild, de Sitter,etc,etc] provide different perspectives.
let's take the first: an inertial observer and an accelerating observer passing by in free space will measure different temperatures...and make different particle counts...because their horizons are different. Similarly, accelerating outside a black hole horizon enables you to observe different temperatures and particles than if you are inertial [free falling]; in the former you get fried by radiation, in the latter you pass the theoretical horizon and are completely unaware of it! Supposedly all that is 'real' .
Next consider this:
... uniquely-defined particle states do not exist in general, in QFT on a curved spacetime. More in general, particle states are difficult to define in a background-independent quantum theory of gravity...we observe that if the mathematical definition of a particle appears somewhat problematic, its operational definition is clear: particles are the objects revealed by detectors, tracks in bubble chambers, or discharges of a photomultiplier…”
that's from Carlo Rovelli, this discussion and his 2004 research paper:
https://www.physicsforums.com/showthread.php?t=386051
http://arxiv.org/abs/gr-qc/0409054
So just post a question, 'What is a particle?", or better yet, see past discussions here, and youll see we have a lot of good ideas, but exactly why we have the particles we do, why they have the characteristics they do, is not really known from fundamental first principles. We know all that stuff because we measure it...not because we have a perfect underlying theory.
Finally, and briefly, the horizons associated with acceleration: The existence, properties, and significance of a cosmological/causal horizon depend on the particular cosmological model being discussed...analogous to my comment above about different spacetimes offering different perspectives.
Here is the way I first thought about particles popping out [becoming real] as a result of the presence of horizons: If you think of virtual particles as real and imaginary numbers, like some solutions to quadratic equations, Consider that the imaginary ones pass through a horizon...so they have no further causal effect..they no longer offset the 'real' number and that becomes a detectable particle. This explanation will draw lots of criticism, I'm sure, but it got me started...so maybe it will benefit you,too. I think I got the idea from the also simplistic description of Hawking radiation where a black hole horizon separates virtual particles with one disappearing behind the horizon and the other emerging as a real [detectable] particle. [This also is an intutive description according to Hawking himself when he tried to figure out what his own math might be suggesting.]